Financial Mathematics for Actuaries (M339W=M389W)
Important external links
Link to the
Sample SoA problems and solutions
- Part I
MFE Exam, Spring 2007: Problems
MFE Exam, Spring 2007: Solutions
MFE Exam, Spring 2009: Problems
MFE Exam, Spring 2009: Solutions
Link to the
Measures of Investment Risk, Monte Carlo Simulation, and Empirical Evidence on the Efficient Markets Hypothesis.
Link to the
Actuarial Applications of Options and Other Financial Derivatives.
Link to the
Sample SoA problems and solutions
- Part II
Link to the
IFM exam tables
Class 1: January 22nd
The binomial asset pricing model [review].
First-Day Handout
Lecture Sixteen: The binomial asset-pricing model.
Class notes
: Review of the binomial asset pricing model.
Class 2: January 24th
Binomial option pricing [review].
Lecture Seventeen: Binomial option pricing.
Lecture Twelve: Gap options
Lecture Thirteen: Exchange options
Problem set #1.
Class notes
: Review of the binomial option pricing.
Last term's prerequisite in-term
--
Problems
Last term's prerequisite in-term
--
Solutions
Homework #1
--
due on Friday, January 31st
Quiz #1
--
due on Monday, January 27th
Class 3: January 27th
Binomial pricing of currency options. Binomial pricing of futures options.
Class notes: Currency and futures options (the binomial model).
Quiz #1
--
Solutions
Quiz #2
--
due on Wednesday, January 29th
Class 4: January 29th
More on futures options. Subjective expectations and forward contracts.
Class notes: Futures options (the binomial model). Subjective expectations.
Class notes
: Subjective expectations. Realized returns.
Quiz #2
--
Solutions
Class 5: January 31st
Subjective expectations and forward contracts[cont'd].
Problem set #2
Scaled random walk. Central limit theorem.
Mathematica Code: One Random Walk
YouTube: One Random Walk
Mathematica Code: Binomial model limit
(In-class) Warm-up #1
--
Solutions
Homework #1
--
Solutions
Class 6: February 3rd
The prerequisite in-term exam
The prerequisite in-term exam
--
Solutions
Class 7: February 5th
Realized returns.
Class notes
: Realized returns.
Class 8: February 7th
The log-normal distribution. Jensen's inequality.
Class notes
: The log-normal distribution. Jensen's inequality.
The Log Normal Distribution
from the
Wolfram Demonstrations Project
by Chris Boucher
Mathematica demonstration: Modeling return distributions
Class 9: February 10th
Log-normal stock prices. Parameter interpretation.
Class notes
: Lognormal stock prices: Mean. Median.
Problem set #3
Quiz #3
--
due on Friday, February 14th
Class 10: February 12th
Measures of risk: variance, semi-variance, VaR.
Wikipedia: Variance. Semi-variance.
Wikipedia: Value at Risk (VaR).
Class notes
: Risk measures: Variance. Semi-variance. Value-at-Risk.
Class 11: February 14th
Log-normal stock prices: Tail probabilities.
Class notes
: Tail probabilities.
Problem set #4
--
Solutions
Quiz #3
--
Solutions
Quiz #4
--
due on Wednesday, February 19th
Homework #2
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due on Monday, February 24th
Class 12: February 17th
Lognormal "confidence" intervals. VaR (revisited).
Class notes
: Lognormal "confidence" intervals. VaR (revisited).
Class 13: February 19th
TVaR. Coherent risk measures.
Class notes
: Tail Value-at-Risk (TVaR). Coherent risk measures.
Wikipedia: Tail Value at Risk (TVaR).
Wikipedia: Coherent risk measures.
Quiz #4
--
Solutions
Class 14: February 21st
Log-normal partial and conditional expectations. Black-Scholes prices.
Class notes
: Log-normal partial and conditional expectations. Black-Scholes prices.
Wikipedia: Black-Scholes
The original article by Black and Scholes
Mathematica Code: Black-Scholes price
Quiz #5
--
due on Wednesday, February 26th
Class 15: February 24th
Black-Scholes prices [cont'd].
Class notes
: Black-Scholes pricing: Calls. Puts. Forward start options.
Black-Scholes prices [cont'd]. The "master" Black-Scholes pricing formula.
Class notes
: Black-Scholes pricing: Rolling insurance strategy. Gap options. The "master" Black-Scholes pricing formula.
Problem set #5
--
Solutions
Homework #2
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Solutions
Class 16: February 26th
Black-Scholes prices: Currency options. Futures options.
Class notes: Black-Scholes pricing: Currency options. Futures options.
Quiz #5
--
Solutions
Class 17: February 28th
Black-Scholes prices: Discrete-dividend-paying stocks.
Class notes: Black-Scholes pricing: Discrete-dividend-paying stocks.
Quiz #6
--
due on Monday, March 2nd
Class 18: March 2nd
Black-Scholes prices: Discrete-dividend-paying stocks [cont'd].
Option Greeks in the Black-Scholes model.
Wikipedia: Greeks
Class notes: Discrete-dividend stocks. Black-Scholes greeks.
Slides: Option Greeks.
In-Term One
--
practice problems
Sample In-Term One
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Solutions
Quiz #6
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Solutions
Class 19: March 4th
Focus on the delta.
Class notes: Focus on the delta
Class 20: March 6th
Option elasticity.
Class notes: Option elasticity.
Suggested Problem: MFE Exam Spring 2007: Problem #5 (option volatility)
Homework #3
--
due on Monday, March 30th
Class 21: March 9th
In-term exam I
In-Term One
--
Solutions
Class 22: March 11th
Focus on gamma. Other greeks.
Class notes: Gamma.
Mathematica Code: Black-Scholes Greeks
YouTube: Black-Scholes Greeks
Class 23: March 13th
UT closed. No classes due to COVID-19.
The
updated
First-Day Handout
Class 24: March 23rd
No classes due to COVID-19.
Class 25: March 25th
No classes due to COVID-19.
Class 26: March 27th
No classes due to COVID-19.
Class 27: March 30th
Getting used to Zoom.
Homework #3
--
Solutions
Class 28: April 1st
Implied volatility.
Wikipedia: Implied volatility.
Class notes: Implied volatility. Delta-gamma-theta approximation.
YouTube: Implied volatility.
Homework #4
--
due on Wednesday, April 8th
Class 29: April 3rd
Delta-gamma-theta approximation.
Class notes: Implied volatility. Delta-gamma-theta approximation.
Market-making and delta-hedging.
Wikipedia: Market maker.
Class notes: Market making. Delta hedging.
Slides: Market making. Delta hedging.
Class 30: April 6th
Delta-hedger's profit.
Class notes: Delta-hedger's profit.
Quiz #10
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due on Friday, April 10th
Class 31: April 8th
Delta-gamma hedging.
Class notes: Delta-gamma hedging.
Homework #4
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Solutions
Quiz #11
--
due on Monday, April 13th
In-Term Two
-- Topics
Sample In-Term Two
-- Problems
Sample In-Term Two
-- Solutions
Class 32: April 10th
Exchange options.
Class notes
: Exchange options.
Quiz #10
--
Solutions
Quiz #12
--
due on Friday, April 17th
Homework #5
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due on Monday, April 20th
Class 33: April 13th
Analyzing the project. Break-even analysis.
Wikipedia: Cost of capital.
Wikipedia: Equity cost of capital.
Wikipedia: Capital budgeting.
Planet money: Spreadsheets!
Class notes
: Break-even analysis.
Quiz #13
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due on Wednesday, April 22nd
Information, competition, and stock prices. The efficient market hypothesis. Historical returns of stocks and bonds. Confidence intervals for the mean return.
Wikipedia: Efficient-market hypothesis.
Class notes
: Information, competition, and stock prices.
Quiz #11
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Solutions
Mock In-Term Two
-- Problems
Mock In-Term Two
-- Solutions
Class 34: April 15th
In-term exam II
In-Term Two
--
Solutions
Class 35: April 17th
The expected return of a portfolio. The volatility of a two-stock portfolio.
The volatility of a large portfolio.
Class notes
: The expected return of a portfolio. The volatility of a two-stock portfolio. The volatility of a large portfolio.
Quiz #12
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Solutions
Class 36: April 20th
Diversification. Choosing an efficient portfolio.
Class notes
: Diversification.
Homework #5
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Solutions
Quiz #14
--
due on Friday, April 24th
Class 37: April 22nd
Feasible sets. Effect of correlation.
Mathematica demonstration: A Two-Asset Markowitz Feasible Set
Mathematica demonstration: A Three-Asset Feasible Set and Efficient Frontier
Class notes
: Feasible sets. Effect of correlation. Sharpe ratio.
Quiz #13
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Solutions
Homework #6
--
due on Wednesday, April 29th
Class 38: April 24th
Sharpe ratio.
Class notes
: Required returns.
Quiz #14
--
Solutions
Quiz #15
--
due on Monday, April 27th
Class 39: April 27th
Required returns. Betas of stocks. The Capital Asset Pricing Model (CAPM): Assumptions.
Class notes
: Required returns.
Wikipedia: CAPM
Quiz #15
--
Solutions
Quiz #16
--
due on Friday, May 1st
Class 40: April 29th
CAPM: Consequences.
Class notes
: CAPM: Consequences.
Quiz #17
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due on Monday, May 4th
Homework #6
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Solutions
Homework #7
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due on Wednesday, May 6th
Class 41: May 1st
Alphas of stocks.
Class notes
: Alphas of stocks.
Wikipedia: Linear regression.
Quiz #16
--
Solutions
Class 42: May 4th
Behavior of individual investors. Systematic trading biases.
Class notes
: Behavior of individual investors.
Quiz #17
--
Solutions
Quiz #18
--
due on Friday, May 8th
An article on familiarity bias.
Familiarity breeds investment.
Wikipedia: Overconfidence effect.
Wikipedia: Disposition effect.
Investopedia: Herd behavior.
Class 43: May 6th
The efficient market hypothesis.
Wikipedia: Efficient-market hypothesis.
Multifactor models.
Class notes
: Multifactor models.
Class notes
: Multifactor models[cont'd].
Wikipedia: Multifactor models.
Wikipedia: The Fama-French model.
Wikipedia: The Carhart four-factor model.
Homework #7
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Solutions
Quiz #19
--
with solutions, not to be handed in
Real options.
Investopedia: Real options.
Class 44: May 8th
SLLN. Monte Carlo simulation.
Wikipedia: Random number generation
Wikipedia: Mersenne twister
Mathematica Code: Unit Uniform
YouTube: Unit uniform
Slides: Probability on Cointoss Space
Class notes
: Binomial stock-price trees with many periods. SLLN. CLT
Law of large numbers. Monte carlo pricing (binomial).
Class notes
: SLLN. Monte Carlo.
Mathematica Code: Binomial Monte Carlo
Quiz #18
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Solutions